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Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation

Authors:

Jian-Qiang HuAuthors Info & Claims

Management Science, Volume 45, Issue 3

Pages 395 - 413

Published: 01 March 1999 Publication History

Abstract

The design of control charts in statistical quality control addresses the optimal selection of the design parameters such as the sampling frequency and the control limits and includes sensitivity analysis with respect to system parameters such as the various process parameters and the economic costs of sampling. The advent of more complicated control chart schemes has necessitated the use of Monte Carlo simulation in the design process, especially in the evaluation of performance measures such as average run length. In this paper, we apply two gradient estimation procedures-perturbation analysis and the likelihood ratio/score function method-to derive estimators that can be used in gradient-based optimization algorithms and in sensitivity analysis when Monte Carlo simulation is employed. We illustrate the techniques on a general control chart that includes the Shewhart chart and the exponentially-weighted moving average chart as special cases. Simulation examples comparing the estimators with each other and with "brute force" finite differences demonstrate the possibility of significant variance reduction in settings of practical interest.

References

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Digital Library

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Cited By

Zhang GPeng YYang S(2021)Gradient-Based Simulation Optimization for Economic Design of Control Charts2021 IEEE 17th International Conference on Automation Science and Engineering (CASE)10.1109/CASE49439.2021.9551514(1979-1984)Online publication date: 23-Aug-2021
https://dl.acm.org/doi/10.1109/CASE49439.2021.9551514
Cui ZFu MHu JLiu YPeng YZhu L(2020)On the Variance of Single-Run Unbiased Stochastic Derivative EstimatorsINFORMS Journal on Computing10.1287/ijoc.2019.089732:2(390-407)Online publication date: 1-Apr-2020
https://dl.acm.org/doi/10.1287/ijoc.2019.0897
Peng YFu MHu JHeidergott B(2018)A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural ParametersOperations Research10.1287/opre.2017.167466:2(487-499)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1287/opre.2017.1674
Show More Cited By

Index Terms

Efficient Design and Sensitivity Analysis of Control Charts Using Monte Carlo Simulation
1. Applied computing
  1. Enterprise computing
2. Mathematics of computing
  1. Probability and statistics
    1. Probabilistic reasoning algorithms
      1. Markov-chain Monte Carlo methods

Index terms have been assigned to the content through auto-classification.

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cover image Management Science

Management Science Volume 45, Issue 3

March 1999

158 pages

ISSN:0025-1909

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INFORMS

Linthicum, MD, United States

Publication History

Published: 01 March 1999

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Cited By

Zhang GPeng YYang S(2021)Gradient-Based Simulation Optimization for Economic Design of Control Charts2021 IEEE 17th International Conference on Automation Science and Engineering (CASE)10.1109/CASE49439.2021.9551514(1979-1984)Online publication date: 23-Aug-2021
https://dl.acm.org/doi/10.1109/CASE49439.2021.9551514
Cui ZFu MHu JLiu YPeng YZhu L(2020)On the Variance of Single-Run Unbiased Stochastic Derivative EstimatorsINFORMS Journal on Computing10.1287/ijoc.2019.089732:2(390-407)Online publication date: 1-Apr-2020
https://dl.acm.org/doi/10.1287/ijoc.2019.0897
Peng YFu MHu JHeidergott B(2018)A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural ParametersOperations Research10.1287/opre.2017.167466:2(487-499)Online publication date: 1-Apr-2018
https://dl.acm.org/doi/10.1287/opre.2017.1674
Ali SPievatolo A(2016)High quality process monitoring using a class of inter-arrival time distributions of the renewal processComputers and Industrial Engineering10.1016/j.cie.2016.01.01294:C(45-62)Online publication date: 1-Apr-2016
https://dl.acm.org/doi/10.1016/j.cie.2016.01.012
özdemir DYücesan EHerer YDunkin AIngalls R(2009)Sample average approximation approach to multi-location transshipment problem with capacitated productionWinter Simulation Conference10.5555/1995456.1995782(2384-2394)Online publication date: 13-Dec-2009
https://dl.acm.org/doi/10.5555/1995456.1995782
Özdemir DYücesan EHerer YNicol DFujimoto R(2006)Multi-location transshipment problem with capacitated production and lost salesProceedings of the 38th conference on Winter simulation10.5555/1218112.1218379(1470-1476)Online publication date: 3-Dec-2006
https://dl.acm.org/doi/10.5555/1218112.1218379
Özdemir DYücesan EHerer YFerrin DMorrice D(2003)Freight simulationProceedings of the 35th conference on Winter simulation: driving innovation10.5555/1030818.1031054(1729-1736)Online publication date: 7-Dec-2003
https://dl.acm.org/doi/10.5555/1030818.1031054

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